Strong solutions of stochastic equations with singular time dependent drift

Krylov NV, Röckner M (2005)
Probability Theory and Related Fields 131(2): 154-196.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Krylov, N.V.; Röckner, MichaelUniBi
Abstract / Bemerkung
We prove existence and uniqueness of strong solutions to stochastic equations in domains G subset of R-d with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local L-q-L-p-integrability of b in R x G with d/ p+ 2/ q < 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function ψ blowing up as G &EXIST; x --> partial derivativeG, we prove that the conditions 2D(t) psi less than or equal to Kpsi, 2D(t)psi + Deltapsi less than or equal to Ke(epsilonpsi), epsilon is an element of [0, 2), imply that the explosion time is infinite and the distributions of the solution have sub Gaussian tails.
Stichworte
distorted Brownian motion; singular drift; strong solutions of; stochastic equations
Erscheinungsjahr
2005
Zeitschriftentitel
Probability Theory and Related Fields
Band
131
Ausgabe
2
Seite(n)
154-196
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/1605208

Zitieren

Krylov NV, Röckner M. Strong solutions of stochastic equations with singular time dependent drift. Probability Theory and Related Fields. 2005;131(2):154-196.
Krylov, N. V., & Röckner, M. (2005). Strong solutions of stochastic equations with singular time dependent drift. Probability Theory and Related Fields, 131(2), 154-196. https://doi.org/10.1007/s00440-004-0361-z
Krylov, N. V., and Röckner, M. (2005). Strong solutions of stochastic equations with singular time dependent drift. Probability Theory and Related Fields 131, 154-196.
Krylov, N.V., & Röckner, M., 2005. Strong solutions of stochastic equations with singular time dependent drift. Probability Theory and Related Fields, 131(2), p 154-196.
N.V. Krylov and M. Röckner, “Strong solutions of stochastic equations with singular time dependent drift”, Probability Theory and Related Fields, vol. 131, 2005, pp. 154-196.
Krylov, N.V., Röckner, M.: Strong solutions of stochastic equations with singular time dependent drift. Probability Theory and Related Fields. 131, 154-196 (2005).
Krylov, N.V., and Röckner, Michael. “Strong solutions of stochastic equations with singular time dependent drift”. Probability Theory and Related Fields 131.2 (2005): 154-196.

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